Chapter 6: Saving for a Child's College Education

Consider the following investment scenario faced by many parents. How much money needs to be saved ahead of time to make sure that enough money will be available for their newborn child's education? Suppose, for example, that $100,000 will be necessary for college expenses when the child turns 18. According to Kay Johnson, a certified financial planner with Provident Wealth Managemnt, Inc., the following two options are generally available to the parents.

Option #1

The new parents could set aside one lump-sum amount today, investing it to earn the prevailing market interest rate so that, with the compounding of interest, the desired level of income would be achieved after 18 years. The concept of present value enables us to compute the lump-sum amount that needs to be invested today. (See Section 6.2 for an explanation of present value, and Section 1.6 for a review of compound interest.)

If P is the amount deposited today and r is the annual interest rate (in decimal form) compounded continuously, then the balance will grow to A in t years according to the formula



This equation can be rearranged to find the amount P that must be deposited today to achieve a specified future value A after t years.



In our example, the new parents want to accumulate $100,000 after 18 years. Assuming an interest rate of 8 percent compounded continuously, the lump- sum deposit they must make today is



Option #2

Many young parents, however, are unable to set aside such a large lump-sum deposit all at once, despite the benefits of compound interest. For them, it might be more feasible to set aside a fixed dollar amount each year, over the course of 18 years. For these families, the question becomes: How much must be saved each year, if interest is compounded continuously, to accumulate $100,000 after 18 years? From Section 6.2 we know that the present value P of a continuous income stream lasting for t₁ years at a constant rate of c dollars per year and an interest rate of r percent, compounded continuously, is



In Option 1 we determined that it would be necessary to deposit $23,692.80 today to achieve the desired $100,000 18 years later. Using $23,692.80 as the present value P in the equation just derived, we may solve for the constant deposit of c dollars per year.





That is, the parents should deposit $2483.94 per year for 18 years in order to have $100,000 available for their child's college education.

For more information on college costs, see www.collegeboard.org/press/cost97/exhibit.html

 

What Would You Do?

1. Calculate the actual savings and interest earned under each of the two options.
2. Redo the above computations if the interest rate is changed from 8% to 10%.
3. What effect would inflation have on the new parents' decisions concerning their savings for the education of their child? Recommend a strategy for overcoming inflation.